# Various Analyses of Variance

There are many statistical analyses of variance that can be performed on data. Perhaps the most widely known is the ANOVA, which plainly stands for analysis of variance. This test compares means from three (or more) groups to determine if there are significant differences in the dependent variable. Let us clarify this with an example. Say you are comparing the self-reported stress levels of video gamers, with different levels of expertise, and want to see if experience predicts stress in players of a particular video game. The ANOVA compares the mean stress scores from novice, hobbyist, and professional gamer groups to see if there is a significant difference in their stress.

Individual groups should be composed of members that have equal levels of experience, and each group’s experience level should be different from the other. All other factors should be equally distributed across the groups to limit noise using random selection. This can help to eliminate problems with assumptions.

Assumptions refers to expectations about your dataset that must be true otherwise the ANOVA cannot be performed. One of these is that the dependent variable (ex, stress scores) in each group must be normally distributed. Normal distribution refers to a spread of data that creates a bell curve with most scores occurring around the mean. A visual example is below.

http://www.itl.nist.gov/div898/handbook/pmc/section5/gifs/normal.gif

Another assumption is that the variance in each group’s stress scores is relatively similar. These first two assumptions are generally passed when random selection is appropriately used to compose your groups. A third assumption, independence of observations, is an issue of design. It requires that observations made on the dependent variable (ex, stress) are collected only once per participant, and no participant tells future participants about the experiment.

With all assumptions met, the test can be performed to compare the scores from each group and to see if any group is statistically different from the others. In our example, we might hypothesize that novice stress is worse than all other groups. An ANOVA will help you as a researcher begin to test this hypothesis.

ANOVA is in some ways a baseline statistical analysis. This means that there are variations on the model, and understanding ANOVA helps to understand those variations. One such analysis is called MANOVA, short for multivariate analysis of variance. Where ANOVA tests one dependent variable against the independent variable, MANOVA tests two dependent variables against the independent variable. Let us make a slight change to the example experiment to get a better understanding. Say you are comparing video gamers with different levels of expertise and want to know if there are significant differences in skin conductance and heart rate between novice, hobbyist, and professional gamers while they play a particular game. In this example, MANOVA would be used.

Another variation is called ANCOVA, short for analysis of covariance. Where ANOVA tests one dependent variable against the independent variable, ANCOVA lets you control for a third variable. Let us again make a slight change to the example experiment to get a better understanding. Say you are comparing video gamers with different levels of expertise and want to know if there are significant differences in heart rate between novice, hobbyist, and professional gamers, mediated by caffeine use, while they play a particular game. In this example, ANCOVA would be used.

With both of these variations described you are well prepared to guess what MANCOVA is short for and what it tests. If curiosity demands, try an internet search to check and see if you are correct.